Unknotting and maximum unknotting numbers

Abstract

We introduce concepts of the maximum unknotting number and the mixed unknotting number, taking into consideration the Bernhard-Jablan Conjecture about computing the unknotting number based only on minimal knot diagrams. The existence of Kauffman knots (alternating knots, such that a crossing change does not change their minimal crossing number) was first suggested by Kauffman. We extend the concept and offer three related classes of knots named: Kauffman knots, Zeković knots and Taniyama knots.